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www.logicmatters.net | ||
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www.umsu.de
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| | | | | [AI summary] The discussion centers on the interpretation of higher-order logic and the role of metaphysical domains. Andrew Bacon argues that higher-order logic doesn't require a metaphysical commitment to domains of objects, properties, or propositions. Instead, he emphasizes the use of stipulative definitions and logical connections between sentences to interpret expressions. He contrasts this with the idea that models must be interpreted in a way that reflects a metaphysical structure of reality. The conversation also touches on the nature of provability operators and their relationship to logical frameworks, highlighting the distinction between formal languages and their interpretations in different contexts. | |
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xorshammer.com
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| | | | | Let $latex \mathrm{PA}$ be Peano Arithmetic. Gödel's Second Incompleteness Theorem says that no consistent theory $latex T$ extending $latex \mathrm{PA}$ can prove its own consistency. (I'll write $latex \mathrm{Con}(T)$ for the statement asserting $latex T$'s consistency; more on this later.) In particular, $latex \mathrm{PA} + \mathrm{Con}(\mathrm{PA})$ is stronger than $latex \mathrm{PA}$. But certainly, given that... | |
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www.lesswrong.com
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| | | | | The Löwenheim-Skolem theorem implies, among other things, that any first-order theory whose symbols are countable, and which has an infinite model, h... | |
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lucatrevisan.wordpress.com
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| | | (This is the sixth in a series of posts on online optimization techniques and their ``applications'' to complexity theory, combinatorics and pseudorandomness. The plan for this series of posts is to alternate one post explaining a result from the theory of online convex optimization and one post explaining an ``application.'' The first two posts were... | ||
